Abstract

We consider a special system of integral equations of convolution type with a monotone convex nonlinearity naturally arising when searching for stationary or limit states in various dynamic models of applied nature, for example, in models of the spread of epidemics, and prove theorems stating the existence or absence of a nontrivial bounded solution with limits at \(\pm \infty \) depending on the values of these limits and on the structure of the matrix kernel of the system. We also study the uniqueness of such a solution assuming that it exists. Specific examples of systems whose parameters satisfy the conditions stated in our theorems are given.

中文翻译：

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关于全实线上卷积型非线性积分方程组的解

摘要

我们考虑一个特殊的卷积型积分方程组，当在各种应用性质的动态模型（例如流行病传播模型）中搜索稳态或极限状态时，自然会出现单调凸非线性，并证明存在性的定理或者不存在限制为 \(\pm \infty \) 的非平凡有界解，具体取决于这些限制的值以及系统矩阵核的结构。我们还假设这种解决方案存在，并研究其独特性。给出了参数满足我们定理中所述条件的系统的具体例子。